Let x1, X2, ... , X, be a random sample from a normal population with unknown mean µ and an unknown variance o2.Construct the generalized likelihood ratio test for Ho : µ 2 µo = 10 versus H1 : 4 < µo at a given significance level a.The following `answers" have been proposed.(a) The test rejects Ho ifnormal density.where c is the value so that to the right of c lies the area of a under the the standard> C,(b) The test rejects Ho if> c,where c is the value so that to the right of c lies the area of a under the i densitywith n –1 degrees of freedom.(c) The test rejects Ho ifnormal density.C,where c is the value so that to the left of c lies the area of a under the the standard(d) The test rejects Ho ifwhere c is the value so that to the left of c lies the area of a under the i density with

Answered: Image /qna-images/answer/d76b7262-4968-4eb4-b5e7-ccf8c8c77022.jpg

Answered: Let x1, X2, ... , Xn be a random sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You wish to test the following claim (Ha) at a significance level of a = 0.05. H,:µ1 = µ2 Ha:µ1 7 42 You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size ni = 18 with a mean of M1 deviation of SD1 = 13.3 from the first population. You obtain a sample of size n2 = 10 with a mean of M2 = 71.3 and a standard deviation of SD2 = 7.8 from the second population. = 63.3 and a standard What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? For this calculation, use the conservative under-estimate for the degrees of freedom as mentioned in the textbook. (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) a greater than a This test statistic leads to a decision to... |reject the…
For the hypothesis test Ho: u = 8 against H1:µ < 8 and variance known, calculate the P-value for each of the following test statistics. Round your answers to two decimal places (e.g. 98.76). (a) zo = 1.81 P-value = (b) zo = -1.84 P-value = (c) zo = 0.33 P-value =
The IE Dept. is interested in the mean age of a certain population. A random sample of 10 individuals drawn from the population has a mean of 27. Assuming that the population is approximately normally distributed with variance 20, can we conclude that the mean is less than 30 years ? (α=0.10) . What is the critical region? -1.28 -1.645 -1.96 -2.33
A severe storm has an average peak wave beight of 16,4 feet for waves hitting the shore. Suppose that a storm is in progress with a severe storm class rating. Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis? Is the P-value area on the left, right, or on both sides of the mean? O H:a is less than 16.4 feet; the P-value area is on the left of the mean O H:u is less than 16.4 feet; the P-value area is on the right of the mean O H: u is greater than 16.4 feet; the P-value area is on the right of the mean OH:u is not equal to 16.4 feet: the P-value area is on the left of the mean OH : u is not cqual to 16.4 feet; the P-value area is on the right of the mean
A random sample of size 24 and mean 2.547 was selected from normal distribution if we want to test that the population mean is less than 5.547, knowing that the sample variance 25, the critical value for alpha =0.01 is? a. 2.807 b. 2.500 c. 2.547 d. 2.33
A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands, an experiment is conducted using 14 of each brand. The tires are run until they wear out. The results are given in the table below. Compute a 90% confidence interval for μA−μB assuming the populations to be approximately normally distributed. You may not assume that the variances are equal. Brand A x1=35,300 kilometers s1=4900 kilometers Brand B x2=37,200 kilometers s2=6100 kilometers
An automatic filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of s2 = 0.0153 (fluid ounces) 2. If the variance of fill volume exceeds 0.01 (fluid ounces)2, an unacceptable proportion of bottles will be underfilled or overfilled. Using a level of significance of 0.05, and assuming that fill volume has a normal distribution, answer the following questions. If χ2critical = 30.14, is there evidence in the sample data to suggest that the manufacturer has a problem with underfilled or overfilled bottles?
is being approxin Let X1,..., Xn be an iid with mean, µ = E(X), and variance, o2 = Var(X). True or False, and briefly explain: The sample average, X, can be expected to be closer and closer to µ as n gets bigger and pigger. Confidence Intervals
A survey of the white and nonwhite population in a local area reveals the following annual trip frequencies to the nearest state park: X̄1 = 4.1 X̄2= 3.1 s21 = 14.3 s22= 12.0 N1= 20 N2= 16 Where the subscript '1' denotes the white population and the dubscript '2' denotes the nonwhite population. (a) assume the variances are equal, and test the null hypothesis that there is no difference between the park-going frequences of whites and nonwhites (d) Associated with the test in part (a), find a 95% confidence interval for the difference in means
In the manufacture of steel rollers to fit an assembly, the external diameter is considered to be a random variable with mean equal to 23 mm and variance equal to 0.0036 cm2. 1.5 is supported standard deviations more than the mean and 3.5 standard deviations below average. A piece with a diameter below such specifications is considered waste, whereas a piece with a diameter larger than specified must be reprocessed. Which is the percentage of pieces that:to. They are being wasted.b. They need to be reprocessed.c. Acceptable.d. If you want to establish that the reprocessing is 5% of the rollers and waste of 1%, than specification limit would recommend.
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